Week 5: Division

 Big Ideas

This week, the focus of our content was division. The concept of division is separating a number into equal groups. Division is the inverse operation of multiplication. Knowledge of multiplication is a prerequisite for completing division, as each basic multiplication fact has a related division one (Reys et al. 2020). As a teacher, I must ensure my students have an understanding of multiplication before teaching division due to the inverse relationship between the two. I also need to make sure I am presenting my students with a variety of division problems using both of the two types of division.


Division can be separated into two types: partition and quotition:



The Language Model


Concept, Skill or Strategy

As mentioned earlier, division and multiplication have an inverse relationship. This is why ‘think multiplication’ is a key strategy in division (Reys et al., 2020). To visualise this, division and multiplication mats can be used:


(Origo One, 2017)

Fact families are also great for showing students the link between multiplication and division. A set of three numbers and four facts make a fact family. Here is an example using 2, 4, and 8:

(Jamieson-Proctor, 2021)

If students know one fact of the four, they really know all four. This shows the link between the two operations.

Misconception

Reys et al. (2020), express that teachers should take caution when involving zero in division, as “dividing zero by some number, and dividing some number by zero are very different situations (p.298). To put this simply, there are only two possible outcomes when dividing by zero:


This misconception means that many students will think any division that includes the number zero will equal zero (as they will think multiplication where this does apply). As a teacher, I can remediate this misconception by physically demonstrating that division by zero is impossible. I can use concrete, real-world materials such as toys or lollies to demonstrate both outcomes of the division of zero.

ACARA

Division is first seen in the Australian curriculum in year 2 (ACMNA032)

Strand: number and algebra
Sub-strand: number and place value

(ACARA, 2021)

Scootle


Divide it up grouping tool is a good interactive resource for children to explore division, specifically if they were learning that sometimes there are remainders when dividing numbers. Students choose their own numbers to enter into the grouping tool, then estimate how many equal packets of pens they could make with their number. This would be appropriate for children at the student language stage and materials stage, as it uses real world objects and language. While there is use of symbols, they are accompanied by student language to explain what the symbols are showing, which can assist with their emerging understanding of language used at the mathematics and symbolic stage.

(Education Services Australia, 2016)


Personally Sourced

This is a fun, hands-on activity children can participate in to help them understand the concept of division. This is appropriate for children who are at the children’s language stage as real-world objects are used to assist children in understanding division as sharing.

(BJU Press Homeschool, 2018)

References

ACARA. (2021). Mathematics. https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

BJU Press Homeschool. (2018). Help your second grader with division. https://blog.bjupress.com/blog/2018/04/19/help-second-grader-division/

Education Services Australia (2016). Divide it up: Grouping tool. https://www.scootle.edu.au/ec/viewing/L2810/index.html

Origo One. (2017). Using grouping sharing mats to model multiplication and division. https://www.youtube.com/watch?v=ZH_K1pn-x9Y&ab_channel=ORIGOONE

Reys, R., Lindquist, M., Lambdin, D., Smith, N., Rogers, A., Cooke, A., Ewing, B., & West. J. (2020). Helping children learn Mathematics (3rd Australian ed.). Milton: John Wiley & Sons.














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